Question

At what point will the lines x= -21 - 2y and x = -39 - 4y intersect? (i need the answer)

Answer 1

The lines intersect at (-3, -9)

Step-by-step explanation

The point where the lines intersect is the solution to the system of equations

`\begin{cases}x=-21-2y \\ x=-39-4y\end{cases}`

We can solve it using the elimination method, which consists in subtracting one equation from the other in order to eliminate one of the variables and obtain only one equation with only one variable:

`\begin{gathered} x=-21-2y \\ - \\ x=-39-4y \\ \text{ ------------------------------} \\ (x-x)=(-21-2y)-(-39-4y) \end{gathered}`

Solving for y:

`\begin{gathered} 0=-21+39-2y+4y \\ 0=18+2y \\ 2y=-18 \\ y=-9 \end{gathered}`

Now we have to replace y = -9 into one of the equations and solve for x:

`\begin{gathered} x=-21-2y \\ x=-21-2(-9) \\ x=-21+18 \\ x=-3 \end{gathered}`

The lines intersect at (-3, -9)